A system for performing acceleration/deceleration control of a given vehicle such that the vehicle follows a preceding vehicle while the headway distance from the preceding vehicle is kept constant is described in Japanese Kokai Patent Application No. 2005-329786. Additionally, there is also a system for performing deceleration control of the given vehicle based on the detected headway distance such that the headway distance from the preceding vehicle is guaranteed. A type of vehicle equipped with plural systems for performing the deceleration control as aforementioned is described in Japanese Kokai Patent Application No. 2007-313932.